Given $ m \angle LOM = 9x - 8$, $ m \angle MON = 7x - 60$, and $ m \angle LON = 108$, find $m\angle LOM$. $O$ $L$ $N$ $M$
Explanation: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Substitute in the expressions that were given for each measure: $ {9x - 8} + {7x - 60} = {108}$ Combine like terms: $ 16x - 68 = 108$ Add $68$ to both sides: $ 16x = 176$ Divide both sides by $16$ to find $x$ $ x = 11$ Substitute $11$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 9({11}) - 8$ Simplify: $ {m\angle LOM = 99 - 8}$ So ${m\angle LOM = 91}$.